Question
Box A has a volume of 216 cubic meters. Box B is similar to box A. To create Box B, Box A's dimensions were divided by 2. What is the volume of Box B?
Answers
GPT-4o mini
Since Box A has a volume of 216 cubic meters and Box B is similar to Box A but with each dimension divided by 2, we can calculate the volume of Box B as follows.
When the dimensions of a three-dimensional object are scaled by a factor, the volume scales by the cube of that factor. In this case, the scaling factor is \( \frac{1}{2} \) (since each dimension is divided by 2).
To find the volume of Box B, we calculate the volume scaling factor:
\[
\text{Volume scale factor} = \left(\frac{1}{2}\right)^3 = \frac{1}{8}
\]
Now we can compute the volume of Box B:
\[
\text{Volume of Box B} = \text{Volume of Box A} \times \text{Volume scale factor} = 216 \times \frac{1}{8} = 27
\]
Thus, the volume of Box B is \( \boxed{27} \) cubic meters.
When the dimensions of a three-dimensional object are scaled by a factor, the volume scales by the cube of that factor. In this case, the scaling factor is \( \frac{1}{2} \) (since each dimension is divided by 2).
To find the volume of Box B, we calculate the volume scaling factor:
\[
\text{Volume scale factor} = \left(\frac{1}{2}\right)^3 = \frac{1}{8}
\]
Now we can compute the volume of Box B:
\[
\text{Volume of Box B} = \text{Volume of Box A} \times \text{Volume scale factor} = 216 \times \frac{1}{8} = 27
\]
Thus, the volume of Box B is \( \boxed{27} \) cubic meters.